- #1
Niles
- 1,866
- 0
Homework Statement
Hi
Please take a look at the following equality found in my book:
[tex]
\left| \mu \right\rangle = \sum\limits_v {\left| v \right\rangle \left\langle {v}
\mathrel{\left | {\vphantom {v \mu }}
\right. \kern-\nulldelimiterspace}
{\mu } \right\rangle } = \sum\limits_v {\left\langle {\mu }
\mathrel{\left | {\vphantom {\mu v}}
\right. \kern-\nulldelimiterspace}
{v} \right\rangle ^* \left| v \right\rangle }
[/tex]
The asterix denotes complex conjugation. I cannot see why the second equality holds, since
[tex]
\sum\limits_v {\left\langle {\mu }
\mathrel{\left | {\vphantom {\mu v}}
\right. \kern-\nulldelimiterspace}
{v} \right\rangle ^* \left| v \right\rangle } = \sum\limits_v {\left\langle {v}
\mathrel{\left | {\vphantom {v \mu }}
\right. \kern-\nulldelimiterspace}
{\mu } \right\rangle \left| v \right\rangle } \ne \sum\limits_v {\left| v \right\rangle \left\langle {v}
\mathrel{\left | {\vphantom {v \mu }}
\right. \kern-\nulldelimiterspace}
{\mu } \right\rangle }
[/tex]
What am I missing here?
Niles.